Problem: Express this product in scientific notation: $(4.20\times 10^{-4})\times (4.00\times 10^{1})$
Explanation: Start by collecting like terms together. $= (4.20\times 4.00) \times (10^{-4}\times 10^{1})$ When multiplying exponents with the same base, add the powers together. $= 16.8 \times 10^{-4\,+\,1}$ $= 16.8 \times 10^{-3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $16.8$ is the same as $1.680 \times 10$ $ = {1.680 \times 10} \times 10^{-3} $ $= 1.680\times 10^{-2}$